Problem: Simplify the following expression: $x = \dfrac{q^2 - 8q + 12}{q - 2} $
First factor the polynomial in the numerator. $ q^2 - 8q + 12 = (q - 2)(q - 6) $ So we can rewrite the expression as: $x = \dfrac{(q - 2)(q - 6)}{q - 2} $ We can divide the numerator and denominator by $(q - 2)$ on condition that $q \neq 2$ Therefore $x = q - 6; q \neq 2$